都市施設の適切な数に関する数理モデル : 政令指定都市の区数に関する分析例

Abstract

A mathematical model on the optimal number of urban facilities is concerned in this paper. The model is to minimize the sum of two types of cost: 1) facilities construction and operation cost and 2) transportation cost from residences to the facilities. The model is formulated under two assumptions: i) the population density is uniform all over the city; ii) each territory of the facility is mutually congruent. One of the main results is as follows : If the construction and running cost of a facility is linear function of the number of allocated users, the optimal number of the facilities is proportional to two-thirds power of the population of the city times the cube root of the area of the city. By this result, we can rationally compare the numbers of facilities of cities whose population and area vary. In this paper, the numbers of wards in the ordinance-designated cities in Japan are empirically examined. Moreover, our study clarifies that the average, cost per capita is the decreasing function of the population density of city. According to this result, we can argue how the consolidation of two cities effects on the average cost per capita.